Searching a Shared Mailbox can have it's limits within the Outlook desktop app, if there is a requirement to search the entire mailbox, please follow the steps below.
Log into the Outlook Web App at https://outlook.office365.com using your own Office 365 credentials (SMU email address/password)
Click on your profile image (or placeholder image) on the top righ
Choose Open another mailbox
Type in the name or email address of the Shared Mailbox and select it. The shared mailbox will open in a new window with the ability to search the mailbox.